X-ray source is usually considered as a monochromatic point source, regardless of whose size effect. However, in clinical practical applications, an X-ray tube is a polychromatic source with a finite focal spot. The incident X-ray source was supposed as the average intensity distribution of a qusi-monochromatic light circular source in the beginning, and then it was extended to the polychromatic case. Based on Fresnel-Kirchhoff diffraction theory, taking the spatial coherence into account, the new in-line X-ray Phase-contrast imaging formula was derived by Fourier transform. The absorption contrast transmission function γre and phase contrast transmission function γre2πλR2u2/M were obtained from the new formula, which represented absorption effect and phase effect, respectively. The curves of the above functions for different radiuses were given by software Matlab and the optimal positions for different source radiuses were also calculated. The theoretical analysis results are as follows: 1) the spatial coherence effect should be considered when source radius is bigger enough, and decreasing the source radius would increase phase effect; 2) there is the definitive relationship between the radius and the optimal imaging position, which has been presented in a special case；3) the effect of source size on phase effect is not infinite, which could be ignored when the size is equal to a suitable value. The suitable radius is given in a special case; 4) decreasing incident X-ray photon energies would strengthen PE obviously, and the variation of photon energies has no effect on the optimal imaging position; as a result, the new formula could be extended to the polychromatic case. In order to verify the theoretical results, the micro-focus X-ray phase-contrast imaging experiments for the breakage surface of optical glass detection were carried out. Some experimental results are in good agreement with theoretical analysis, while some do not meet our expectations. The related explanations were also presented.